%1/96
\documentstyle[12pt]{article}
\pagestyle{empty}

\input /u/disk12/ma/rbrown/tex/macros/latex_course.tex
\input rmb_local.tex

\textwidth 6in
\oddsidemargin 0.25in
\topmargin-0.25in
\textheight 8.5in
\begin{document}

\vspace{-1 in}
\begin{flushleft} 
{\course}         \hfill {Instructor: Russell Brown}\\ 
{\daytime }	  \hfill {Office: POT741} \\
{\room}	          \hfill	{Phone: 257-3951}\\
{\semester}	  \hfill	rbrown@ms.uky.edu\\
        	  \hfill	{MF11--12, W2--3}\\
                  \hfill        {and by appointment.}

\medskip	

\hd{Grading}  \begin{tabular}[t]{l} 
Mid term  exam 100 \\ 
Homework 150\\
Final 200
\end{tabular}

\hd{Text} {\it Principles of mathematical analysis, 3rd edition } by
Walter Rudin.

This is a course intended to introduce beginning graduate students in
mathematics to the basic techniques of analysis. 

\hd{Homework} 
Homework will be assigned and collected regularly.  You should
endeavor to write out your homework clearly. Use complete
sentences.  Refer to facts from the text by giving page or result numbers.

Be aware that your instructor is old and cranky. 
Late homework will not  be accepted.   You may only write on one side
of a paper. Leave 
generous margins. I may use the margins and the back of each sheet for
comments. 
I prefer that your solutions be handwritten. You have enough to do
without the effort of typing homework solutions in latex.


\hd {Exams}  There will be  one midterm  exam and a final.  The final will be
cumulative. The exams will consist of questions similar to those given
on homework. You will be expected to know the main theorems, proofs
and definitions of the course.  You should not only commit these to
memory, but you should be able to provide examples to illustrate them.

The departmental cease-fire and fall break will be observed 10/3--10/5.

The final exam  is at 10:30am--12:30pm, Monday, 15 December.

A number of other  textbooks cover  the material of this course. 
The following will be on reserve in the library.  You may want to
refer to them. 

\begin{itemize} \item \em The way of analysis, \rm Robert Strichartz
\\
\item \em Introduction to mathematical analysis, \rm Steven Douglas\\
\item \em Calculus, \rm Michael Spivak \\
\end{itemize}

\hd{Schedule} Below is a tentative list of sections to be covered. The
topics correspond to the section headings in Rudin's book.

\begin{tabular}{lp{3.5in}l}
Chapter & Topics & Dates \\ 
1       & Introduction, Ordered sets, fields, the real field, the
extended real number system, the complex field, Euclidean spaces &
8/27--9/4 \\
2   & Finite, countable, and uncountable sets, metric spaces, compact
sets, connected sets & 9/8-- 9/19 \\
3 & Convergent sequences, subsequences, Cauchy sequences, upper and
lower limits, some special sequences, series, series of non-negative
terms, the number $e$, the root and ratio tests & 9/22-10/10 \\
  & Review, exam & 10/13, 10/15 \\
4 & Limits of functions, continuous functions, continuity and
compactness, continuity and connectedness, discontinuities, monotonic
functions, infinite limits and limits at infinity & 10/17--10/31 \\
5 & The derivative of a real function, mean value theorems, the
continuity of derivatives, l'hopital's rule, derivatives of higher
order, Taylor's theorem   &  11/3--11/14  \\
6 & Definition and existence of the integral, properties of the
integral, integration and differentiation & 11/17--11/24
\\
7 &  Discussion of main problem, uniform convergence, uniform
convergence and continuity, uniform convergence and integration,
uniform convergence and differentiation, equicontinuous families of
functions, the Stone-Weierstrass theorem  & 11/26--12/12
\end{tabular}

 
\smallskip


\end{flushleft}
\end{document}
